On the Complexity of a Charged Quantum Oscillator

TL;DR

This paper investigates how electric and magnetic fields influence the complexity growth rate of a charged quantum oscillator, revealing that electric fields decrease while magnetic fields increase the rate, with a critical magnetic field value causing a behavioral shift.

Contribution

It provides a novel analysis of the effects of electromagnetic fields on quantum complexity growth in a charged oscillator system.

Findings

Electric field decreases the complexity growth rate.

Magnetic field increases the complexity growth rate.

A critical magnetic field value causes a drastic change in behavior.

Abstract

In this paper, we study the effect of both the electric and the magnetic fields on the rate of complexity growth. Our system is a charged quantum oscillator and over a period of time, we study the maximum dynamic evolution of quantum states which might lead to a strong bound on the rate of computation. We show that by turning on the electric field, the rate of complexity decreases whereas this rate has increasing behavior when the magnetic field is turned on. In this regard, we also find a critical value of the magnetic field, beyond which this rate changes its behavior drastically.